Since the first application of an optical fiber interferometer as a means of detecting an acoustical signal, there have been a long series of improvements to the sensitivity, selectivity, and robustness of this fiber-optic sensor strategy. (Bucaro el al, "Fiber optic hydrophone", J. Acoust. Soc. Am 62, 1302 (1977)). This development has resulted in the fabrication of fiber-optic acoustic and vibration sensors which are capable of reaching the phenomenological limitations of this technology imposed by the elastic properties of optical fibers and the unavoidable noise introduced by thermal fluctuations. (Gardner et al, "Fiber optic seismic sensor", Fiber Optic and Laser Sensors V, Proc. Soc. Photo Optical Inst. Eng. (SPIE) 838, 271-278 (1987); Garrett et al, "Multiple axis fiber optic interferometric seismic sensor", U.S. Pat. No. 4,893,930 (Jan. 16, 1990); Danielson et al, "Fiber optic ellipsoidal flextensional hydrophones", J. Lightwave Tech. LT-7(12), 195-2002 (1989); Garrett et al, "Flextensional hydrophones", U.S. Pat. No. 4,951,271 (Aug. 21, 1990); Garrett et al, "A general purpose fiber-optic interferometric hydrophone made of castable epoxy", Fiber Optic and laser Sensors V.III, Proc. Soc. Photo Optical Inst. Eng. (SPIE) 1367, 13-29 (1990); U.S. Pat. No. 4,959,539 (Sept. 25, 1990); Hofler et al, "Thermal noise in a fiber-optic sensor", J. Acoust. Soc. Am. 84(2), 471(1988); J. Acoust. Soc. Am. 87(3), 1363 (1990).) In order to produce a complete fiber-optic interferometric sensing system, one must also provide a light source and an opto-electronic receiver/demodulator, in addition to the sensor.
The receiver/demodulator converts the time varying optical power into a representation (analog or digital) of the original stimulus. The optical power modulations contain the information about the measurand that has been encoded as an optical phase modulation by the interferometric sensor. Ideally, this conversion creates a signal which is linearly proportional to the measurand. This conversion of the optically encoded signal back into a linear representation of the stimulus is by no means trivial. The optical signal may contain frequency components which are hundreds of times higher than those in the measurand signal for large signals which create many interference fringes for each cycle. For small signals which do not create a complete fringe, it may not even contain the fundamental signal frequency of the signal of interest. Furthermore, the demodulator should be able to compensate for fluctuations in the amplitude of the light source and drifts in the polarization of the light within the interferometer and other changes which might effect the interferometric fringe visibility (also known as the modulation depth) and the total optical power received by the demodulator.
The particular choices for these three components of the interferometric sensor system (i.e., the sensor, light source, and demodulator) are not independent. For example, a pseudo-heterodyne demodulation system using a phase generated carrier, requires that the sensing interferometer have an optical path imbalance and that the semiconductor laser diode light source wavelength be modulated, usually as a result of modulation of the current through the laser diode. These interlocked choices also effect the overall system performance. (Dandridge et al, "Homodyne demodulation scheme for fiber optic sensors using phase generated carrier", IEEE J. Quantum Electron. QE-18, 1647 (1982)) For example, a small path length imbalance will require large amplitude current modulation of the diode laser which leads to mode hopping and excess noise. Alternatively, if the path length imbalance is increased in order to reduce the laser diode current modulation requirement, then a laser with a longer coherence length must be used to insure that interference will still take place. Long coherence length laser diodes are expensive. In addition, the interferometer noise is also linearly proportional to the path length mismatch for a given amount of laser phase noise, so increases in the path length mismatch also introduce excess noise. (Dandridge et al, "Phase noise of single-mode diode lasers in interferometric systems", Appl. Phys. Lett. 17, 937 (1981))
The problems associated with the pseudo-heterodyne demodulation and other schemes which require a "carrier" signal and are not limited to the conflicting requirements for the light source, sensor, and demodulator. There are other technological difficulties which also degrade both the utility and the performance of these demodulators. These include system set-up complexity, dynamic range limitations, and scale factor instability. Although a detailed discussion of these problems would be beyond the scope of this disclosure, it is at least worth identifying their common phenomenological root.
The interferometric output, represented by the current, i, generated by the photodetector that receives the optical output of the coupler, can be expressed as the sum of an infinite series of Bessel Functions as shown below, ##EQU1## where .phi..sub.d is the quasi-static phase difference between the electric field vectors in the two legs of the interferometer and .phi..sub.s is the magnitude of the phase modulation, at angular frequency, .omega., which was induced in the sensor by the measurand. Heterodyne demodulation techniques introduce a "carrier signal" which consists of a phase modulation of amplitude .phi..sub.m, and of frequency .omega..sub.m, which must be at least a factor-of-two higher than the highest frequency of interest generated by the measurand. The amplitude of the carrier phase modulation (or operationally, the amplitude of the laser diode current modulation) is usually chosen so that two adjacent Bessel function components in the series, for example J.sub.1 and J.sub.2, or J.sub.2 and J.sub.3, have equal amplitude. The signal of interest then appears as side-bands on the carrier frequency and its harmonics.
These side-bands can then be "stripped" off of the carrier to provide an in-phase and quadrature signal which can be used to reconstruct the measurand by a conventional sine-cosine demodulation process which involves differentiation, cross-multiplication, summing, and integration. The sine-cosine reconstruction algorithm is based on the Pythagorean trigonometric identity, sin .sup.2 .theta.+cos .sup.2 .theta.=1. The differentiation of each of the signals produces an output which is proportional to the time derivative d.theta./dt. The cross-multiplication and summation produces the constant times the derivative, (d.theta./dt) (sin .sup.2 .theta.+cos .sup.2 .theta.). Integration of d.theta./dt with respect to time then recovers the phase modulation signal of interest, .theta..
Although the heterodyne demodulation process described above seems relatively straight-forward to one skilled in the art, there are many practical difficulties in its implementation, some of which are rather subtle. Since the previous process uses only two harmonics of the infinite series of harmonics, the total optical power is not available unless some other means is employed to obtain that parameter. This means that the process cannot compensate for fluctuations in the laser power or the interferometric fringe visibility. This leads to variations in the scale factor which characterizes the circuit's conversion of optical phase in radians to electrical output in volts. There is no way, in principal, to differentiate between a change in demodulator scale factor and a change in the amplitude of the measurement if a calibration signal is not inserted into the system.
Also, in the previous discussion no mention was made of how the chosen pair of Bessel function amplitudes were set equal and how their equality was to be maintained. In the present implementation of the pseudo-heterodyne demodulators (also called "passive homodyne" demodulators), the adjustment of the Bessel function amplitudes and the determination of their orthogonality (i.e. establishment of the "pure" in-phase and quadrature relationship) is done by a skilled technician. This adjustment typically requires the use of a Fast Fourier Transform (FFT) signal analyzer to adjust the Bessel amplitudes and an oscilloscope in the Lissajous mode to determine the orthogonality. Periodic re-adjustments must be made to compensate for drifts in the light source and the interferometer. The scale factor will again be a function of both the Bessel function equality and orthogonality. Though it should be possible in the future to make these adjustments, now done by a skilled technician, using some automatic feed-back control system, this would again add to the complexity and cost of the required circuitry. If it were simple, it would already have been done!
Finally, the use of the phase modulation of the carrier places a limit on the dynamic range of the heterodyne demodulator. As stated before, large signals create frequency components which can be higher harmonics of the signal of interest. Since the frequency spacing of the carrier frequency harmonics is .omega..sub.m the demodulation algorithm fails when the signal of interest contains frequency components which are greater than or equal to .omega..sub.m /2 because the lower side-bands of the upper carrier would become indistinguishable from the upper side-bands of the lower carrier. One cannot arbitrarily increase .omega..sub.m in order to increase the dynamic range since thermal time constants of the laser diodes restrict current induced wavelength modulation frequencies to about 100 Khz. Due to this dynamic range limitation, most of the heterodyne fiber optic sensor demodulators have been restricted to low phase rates and hence have had to produce acceptable dynamic ranges (.apprxeq.120 dB) by being able to detect very low amplitude phase modulations (.apprxeq.1-10 .mu.rad/.sqroot.Hz).
From the previous discussion of the sine-cosine demodulation process, it should be apparent that two signals (i.e. in-phase and quadrature) which contain the phase information are required to reconstruct the measurand. In the heterodyne demodulator, this was accomplished by using the side-bands of two carrier harmonics. Another approach which has been used to produce the in-phase and quadrature signals is an interferometer that employs a [3.times.3] coupler as the output coupler. (A. Dandridge, "Fiber optic sensors based on the Mach-Zender and Michelson interferometers", in Fiber Optic Sensors: An Introduction for Engineers and Scientists, Eric Udd, editor (Wiley-Interscience, 1991), Chap. 10) Due to energy conservation, the outputs of a [2.times.2] coupler are 180.degree. out-of-phase. When one of the [2.times.2] outputs is at its maximum, the other must be a minimum, since the total optical power out of the coupler, which is a passive device, must be constant for a constant input power. In an ideal, symmetric (i.e. equal split ratio) [3.times.3] coupler, the outputs have a relative phase difference of 120.degree..
In the previous attempts to produce a demodulator using the outputs of a [3.times.3] coupler, two of these three outputs were combined in order to produce the in-phase and quadrature signals which would then be processed by the sine-cosine demodulation algorithm described in the previous sub-section. (K. P. Koo, A. B. Tveten, and A. Dandridge, "Passive Stabilization Scheme for Fiber Interferometry Using (3.times.3) Fiber Directional Couplers, Appl. Phys. Lett. 41, 616 (1982)) If we represent two of the three outputs from the [3.times.3] coupler, I.sub.2, and I.sub.3, as shown below, EQU I.sub.2 =B.sub.1 +B.sub.2 cos .DELTA..phi.+B.sub.3 sin .DELTA..phi.(2) EQU I.sub.3 =B.sub.1 +B.sub.2 cos .DELTA..phi.-B.sub.3 sin .DELTA..phi.(3)
then by forming their sum and difference, EQU I.sub.2 +I.sub.3 =2B.sub.1 +2B.sub.2 cos .DELTA..phi. and I.sub.2 -I.sub.3 =2B.sub.3 sin .DELTA..phi. (4)
the in-phase (cos .DELTA..phi.) and quadrature (sin .DELTA..phi.) signals can be obtained after gain adjustment and offset subtraction.
Although the use of the [3.times.3] coupler to produce the in-phase and quadrature signal eliminates the problems of the heterodyne approach such as light source wavelength modulation, the required optical path imbalance, Bessel function balance and orthogonality, and the intrinsic dynamic range limitations, the [3.times.3] homodyne demodulation using only two of the three outputs to produce inputs for the sine-cosine algorithm has its own limitations. Again, the total power is not available, since only two of the outputs were utilized, hence no compensation is included for light source power variations or changes in fringe visibility. The lack of symmetry in the demodulation process also reduces the robustness of the algorithm against fluctuations in the split ratio, which is assumed to be equal for each of the three outputs.
It is within this context, and in response to the recent availability of [3.times.3] with good environmental stability and polarization insensitivity, that the new "Symmetric Demodulator for Optical Fiber Interferometers with [3.times.3] Outputs" was developed. (Davis et al, "Characterization of 3.times.3 Fiber Couplers for Passive Homodyne Systems: Polarization and Temperature Sensitivity", paper WQ2, Proc. Optical Fiber Communications Conference, Houston, Tex., Feb. 6-9, 1989)